The role of the dipole-dipole interaction in quasi-one-dimensional antiferromagnets is investigated within a Heisenberg model with nearest-neighbor exchange. We deal with systems in which the magnetic ions are located on a hexagonal lattice, i.e., frustration is present when three-dimensional order sets in. We perform a ground-state calculation for different ratios of dipolar energy to interchain-exchange energy and find several commensurate and incommensurate phases. This is a consequence of the competing character of these two interactions. For the commensurate phases the influence of fluctuations is studied by means of linear spin-wave theory. It turns out that all commensurate phases are stable against fluctuations. The theoretical spin-wave spectra are compared with experiments on ${\mathrm{CsMnBr}}_3$ and ${\mathrm{RbMnBr}}_3.$ The results suggest that the most important source of anisotropy in these Mn compounds is the dipole-dipole interaction. Furthermore the magnetic phase-diagram for small dipolar energies is investigated. A spin-wave calculation allows one to calculate the influence of the fluctuations on physical properties like ground-state energy and magnetization. These results compare favorably with measurements on ${\mathrm{CsMnBr}}_3.$

• Received 30 December 1999

DOI:https://doi.org/10.1103/PhysRevB.63.094425